I don't know about your university specifically, but my uni has a fairly small, tight-knit physics department so the students and professors all get to know each other fairly well fairly quickly. I frequent just barge into a few of my lecturers offices to chat to them completely uninvited (obviously I won't do so if they're very clearly busy) and they're almost always happy to chat (sometimes they'll stop me in the corridor to chat to me).
I guess it all just depends on the nature of your university, the individual professors themselves, etc, etc. I guess the only way to find out is to try! I would say in general people respect initiative and if you're polite and enthusiastic then your introducing yourself to them will probably be fairly well received!
Best of luck.